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Block #2,656,103

TWNLength 12β˜…β˜…β˜…β˜…β˜†

Bi-Twin Chain Β· Discovered 5/10/2018, 6:33:19 PM Β· Difficulty 11.6960 Β· 4,184,058 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
75fe128f763f4fe88242d81d8134978705576637685bc086f4e5922dfac0f6c0
View on Chainz β†—

Height

#2,656,103

Difficulty

11.695965

Transactions

2

Size

689 B

Version

2

Bits

0bb22ac8

Nonce

1,639,846,806

Timestamp

5/10/2018, 6:33:19 PM

Confirmations

4,184,058

Mined by

⛏️ P2SHAMaRndd7EegUdybPg3VAJx9xii9dTWuWQg

Merkle Root

c141abf1a847c3c63a5dc45f768c1be44464dec1c9128d78dcb3dbd60aa0a90e
Transactions (2)
Coinbasec64e6007b7d5b9…b69675ef1f248b
1 in β†’ 1 out7.3100 XPM110 B
AMaRndd7…9dTWuWQg
e4b2c45e08029c…1f8e1d2f365c49
3 in β†’ 1 out10299.9900 XPM489 B
AZFZtVao…Bge3kTNy
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.

1.563 Γ— 10⁹⁴(95-digit number)
15632826780995980003…67821568797966264239
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
1.563 Γ— 10⁹⁴(95-digit number)
15632826780995980003…67821568797966264239
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.563 Γ— 10⁹⁴(95-digit number)
15632826780995980003…67821568797966264241
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
3.126 Γ— 10⁹⁴(95-digit number)
31265653561991960007…35643137595932528479
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
3.126 Γ— 10⁹⁴(95-digit number)
31265653561991960007…35643137595932528481
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
6.253 Γ— 10⁹⁴(95-digit number)
62531307123983920014…71286275191865056959
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
6.253 Γ— 10⁹⁴(95-digit number)
62531307123983920014…71286275191865056961
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
1.250 Γ— 10⁹⁡(96-digit number)
12506261424796784002…42572550383730113919
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.250 Γ— 10⁹⁡(96-digit number)
12506261424796784002…42572550383730113921
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
2.501 Γ— 10⁹⁡(96-digit number)
25012522849593568005…85145100767460227839
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
2.501 Γ— 10⁹⁡(96-digit number)
25012522849593568005…85145100767460227841
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
5.002 Γ— 10⁹⁡(96-digit number)
50025045699187136011…70290201534920455679
Verify on FactorDB β†—Wolfram Alpha β†—
2^5 Γ— origin + 1
5.002 Γ— 10⁹⁡(96-digit number)
50025045699187136011…70290201534920455681
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:57,965,608 XPMΒ·at block #6,840,160 Β· updates every 60s
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