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Block #2,573,068

TWNLength 12β˜…β˜…β˜…β˜…β˜†

Bi-Twin Chain Β· Discovered 3/18/2018, 10:53:57 PM Β· Difficulty 10.9950 Β· 4,260,934 confirmations

TWN
Bi-Twin Chain

Interleaved pairs of primes that differ by 2, forming twin prime pairs at each level.

Block Header
Block Hash
e0a878d3daebcc082482176ca3c736b9cfc8e8ebad0d4b402f0552874ed3b63b
View on Chainz β†—

Height

#2,573,068

Difficulty

10.995026

Transactions

2

Size

424 B

Version

2

Bits

0afeba07

Nonce

81,077,423

Timestamp

3/18/2018, 10:53:57 PM

Confirmations

4,260,934

Mined by

⛏️ P2SHAKsMut8anbSuh9rFAg2Nh1cYpzYXJCJXzr

Merkle Root

a888d5cde8f7b3cc0f84f7f8bc613b19c113d59909c9ec1ec8ff98ee2a74cc09
Transactions (2)
Coinbase00eef79b961868…6cb938275a2207
1 in β†’ 1 out8.2700 XPM109 B
AKsMut8a…YXJCJXzr
bc4336b9dd00c1…8de33416d552fa
1 in β†’ 2 out1155.7784 XPM225 B
AMmJaKps…nCE7eK7cAGGn6SJu…QVxKbSrU
Prime Chain Origin

This is the prime chain origin stored in the block header. It is a composite number (not prime itself) β€” it equals the first prime in the chain multiplied by a primorial. The origin anchors the entire chain to this specific block.

1.338 Γ— 10⁹⁴(95-digit number)
13381327148154368153…63980071720851983119
Discovered Prime Numbers
Lower: 2^k Γ— origin βˆ’ 1 | Upper: 2^k Γ— origin + 1

These are the actual prime numbers discovered by this block, computed using the verified Primecoin formula. Each number has been independently confirmed to pass the Fermat primality test. Use the FactorDB links to verify any number independently.

Level 0 β€” Twin Prime Pair (origin Β± 1)
origin βˆ’ 1
1.338 Γ— 10⁹⁴(95-digit number)
13381327148154368153…63980071720851983119
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.338 Γ— 10⁹⁴(95-digit number)
13381327148154368153…63980071720851983121
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: origin + 1 βˆ’ origin βˆ’ 1 = 2 (twin primes βœ“)
Level 1 β€” Twin Prime Pair (2^1 Γ— origin Β± 1)
2^1 Γ— origin βˆ’ 1
2.676 Γ— 10⁹⁴(95-digit number)
26762654296308736306…27960143441703966239
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.676 Γ— 10⁹⁴(95-digit number)
26762654296308736306…27960143441703966241
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^1 Γ— origin + 1 βˆ’ 2^1 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 2 β€” Twin Prime Pair (2^2 Γ— origin Β± 1)
2^2 Γ— origin βˆ’ 1
5.352 Γ— 10⁹⁴(95-digit number)
53525308592617472613…55920286883407932479
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
5.352 Γ— 10⁹⁴(95-digit number)
53525308592617472613…55920286883407932481
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^2 Γ— origin + 1 βˆ’ 2^2 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 3 β€” Twin Prime Pair (2^3 Γ— origin Β± 1)
2^3 Γ— origin βˆ’ 1
1.070 Γ— 10⁹⁡(96-digit number)
10705061718523494522…11840573766815864959
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.070 Γ— 10⁹⁡(96-digit number)
10705061718523494522…11840573766815864961
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^3 Γ— origin + 1 βˆ’ 2^3 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 4 β€” Twin Prime Pair (2^4 Γ— origin Β± 1)
2^4 Γ— origin βˆ’ 1
2.141 Γ— 10⁹⁡(96-digit number)
21410123437046989045…23681147533631729919
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
2.141 Γ— 10⁹⁡(96-digit number)
21410123437046989045…23681147533631729921
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^4 Γ— origin + 1 βˆ’ 2^4 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 5 β€” Twin Prime Pair (2^5 Γ— origin Β± 1)
2^5 Γ— origin βˆ’ 1
4.282 Γ— 10⁹⁡(96-digit number)
42820246874093978090…47362295067263459839
Verify on FactorDB β†—Wolfram Alpha β†—
2^5 Γ— origin + 1
4.282 Γ— 10⁹⁡(96-digit number)
42820246874093978090…47362295067263459841
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^5 Γ— origin + 1 βˆ’ 2^5 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)

What this block proved

The miner who found this block proved the existence of 12 consecutive prime numbers forming a Bi-Twin Chain. The prime chain origin β€” the large number shown above β€” anchors the chain and is divisible by a primorial (the product of small primes), cryptographically tying these prime numbers to this specific block.

β˜…β˜…β˜…β˜…β˜†
Rarity
ExceptionalChain length 12

Around 1 in 10,000 blocks. A significant mathematical achievement.

How Primecoin's Proof-of-Work Constructs These Primes

Primecoin stores a value called the prime chain origin in each block. The miner found a large integer such that when divided by a primorial (the product of small primes: 2 Γ— 3 Γ— 5 Γ— 7 Γ— …), the result is the first prime in the chain. The origin is deliberately divisible by this primorial β€” that divisibility is part of the proof.

Prime Chain Origin = First Prime Γ— Primorial (2Β·3Β·5Β·7Β·11·…)
Source: Primecoin prime.cpp β€” CheckPrimeProofOfWork()

This is why the origin has many small prime factors β€” those factors are the primorial divisor. The chain then extends from the first prime using the TWN formula:

TWN: twin pairs (p, p+2) where p = origin/primorial βˆ’ 1 and p+2 = origin/primorial + 1
Cross-reference on Chainz Explorer
Circulating Supply:57,916,243 XPMΒ·at block #6,834,001 Β· updates every 60s
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