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Block #2,651,486

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 5/6/2018, 8:46:22 PM Β· Difficulty 11.7510 Β· 4,182,105 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
3906529482c529bb4595e01e2f5762a8378763fa7cd48ec3e28fe8ecc67cfc77
View on Chainz β†—

Height

#2,651,486

Difficulty

11.751011

Transactions

1

Size

201 B

Version

2

Bits

0bc04248

Nonce

1,046,984,472

Timestamp

5/6/2018, 8:46:22 PM

Confirmations

4,182,105

Mined by

⛏️ P2SHAYNwy3nFVtyjctykDzSQ9NBnR96iVARMVn

Merkle Root

695dbc524e7d178da072ee95aeed96330dafff60166e0c2cf1b95784f375723a
Transactions (1)
Coinbase695dbc524e7d17…b95784f375723a
1 in β†’ 1 out7.2300 XPM110 B
AYNwy3nF…6iVARMVn
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.

2.545 Γ— 10⁹⁢(97-digit number)
25455262444898640949…86331947482753433599
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
2.545 Γ— 10⁹⁢(97-digit number)
25455262444898640949…86331947482753433599
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.545 Γ— 10⁹⁢(97-digit number)
25455262444898640949…86331947482753433601
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
5.091 Γ— 10⁹⁢(97-digit number)
50910524889797281899…72663894965506867199
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
5.091 Γ— 10⁹⁢(97-digit number)
50910524889797281899…72663894965506867201
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
1.018 Γ— 10⁹⁷(98-digit number)
10182104977959456379…45327789931013734399
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.018 Γ— 10⁹⁷(98-digit number)
10182104977959456379…45327789931013734401
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
2.036 Γ— 10⁹⁷(98-digit number)
20364209955918912759…90655579862027468799
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.036 Γ— 10⁹⁷(98-digit number)
20364209955918912759…90655579862027468801
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
4.072 Γ— 10⁹⁷(98-digit number)
40728419911837825519…81311159724054937599
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
4.072 Γ— 10⁹⁷(98-digit number)
40728419911837825519…81311159724054937601
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
8.145 Γ— 10⁹⁷(98-digit number)
81456839823675651039…62622319448109875199
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 11 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
RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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:57,912,935 XPMΒ·at block #6,833,590 Β· updates every 60s
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