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Block #2,654,745

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 5/9/2018, 2:33:28 PM Β· Difficulty 11.7147 Β· 4,176,245 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
3e41be119dc2780610b372919f4afe5dc45181b5e29672b1a617230cffc962a6
View on Chainz β†—

Height

#2,654,745

Difficulty

11.714705

Transactions

1

Size

201 B

Version

2

Bits

0bb6f6e6

Nonce

340,043,580

Timestamp

5/9/2018, 2:33:28 PM

Confirmations

4,176,245

Mined by

⛏️ P2SHAWN3Uc7WCxdTG4vZ92jKeAcnt13qYNgYM2

Merkle Root

1f7623711e913de8d4bbb667a7c63b86073bc4efbdba7cb91a9b3135f5983d35
Transactions (1)
Coinbase1f7623711e913d…9b3135f5983d35
1 in β†’ 1 out7.2700 XPM110 B
AWN3Uc7W…3qYNgYM2
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.

1.712 Γ— 10⁹⁷(98-digit number)
17126596225348161028…33965534222223810559
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
1.712 Γ— 10⁹⁷(98-digit number)
17126596225348161028…33965534222223810559
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.712 Γ— 10⁹⁷(98-digit number)
17126596225348161028…33965534222223810561
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
3.425 Γ— 10⁹⁷(98-digit number)
34253192450696322057…67931068444447621119
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
3.425 Γ— 10⁹⁷(98-digit number)
34253192450696322057…67931068444447621121
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
6.850 Γ— 10⁹⁷(98-digit number)
68506384901392644114…35862136888895242239
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
6.850 Γ— 10⁹⁷(98-digit number)
68506384901392644114…35862136888895242241
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
1.370 Γ— 10⁹⁸(99-digit number)
13701276980278528822…71724273777790484479
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.370 Γ— 10⁹⁸(99-digit number)
13701276980278528822…71724273777790484481
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
2.740 Γ— 10⁹⁸(99-digit number)
27402553960557057645…43448547555580968959
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
2.740 Γ— 10⁹⁸(99-digit number)
27402553960557057645…43448547555580968961
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
5.480 Γ— 10⁹⁸(99-digit number)
54805107921114115291…86897095111161937919
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
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