Block #2,647,691

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 5/4/2018, 1:51:10 AM · Difficulty 11.7615 · 4,185,660 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

3965e9c0ba33bb6441da23cfb7401c758e8a20155f27ab6314c39670664e0d91

View on Chainz ↗

Height

#2,647,691

Difficulty

11.761524

Transactions

Size

506 B

Version

Bits

0bc2f342

Nonce

1,755,637,182

Timestamp

5/4/2018, 1:51:10 AM

Confirmations

4,185,660

Mined by

⛏️ P2SHAHNdxxcsWp4SVC62ArdWbVrjCFYUcDQs9k

Merkle Root

720a77d27eac4684280fd865b6adf28d0b3e1610c91ae09dd69ba2b41b822387

Transactions (2)

Coinbaseeba90cf0bce53d…cb585e36f75132

1 in → 1 out7.2300 XPM110 B

AHNdxxcs…YUcDQs9k

250068053085c4…88590b9edfa0ca

2 in → 2 out14.5500 XPM306 B

AGFr4j8Y…qKCuGfiy AWLTrfcT…UUnkvkTp

Prime Chain Origin

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

7.140 × 10⁹⁵(96-digit number)

71403383185105434132…28971781578113146879

Discovered Prime Numbers

Lower: 2^k × origin − 1 | Upper: 2^k × 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 — Twin Prime Pair (origin ± 1)

origin − 1

7.140 × 10⁹⁵(96-digit number)

71403383185105434132…28971781578113146879

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

7.140 × 10⁹⁵(96-digit number)

71403383185105434132…28971781578113146881

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: origin + 1 − origin − 1 = 2 (twin primes ✓)

Level 1 — Twin Prime Pair (2^1 × origin ± 1)

2^1 × origin − 1

1.428 × 10⁹⁶(97-digit number)

14280676637021086826…57943563156226293759

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.428 × 10⁹⁶(97-digit number)

14280676637021086826…57943563156226293761

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^1 × origin + 1 − 2^1 × origin − 1 = 2 (twin primes ✓)

Level 2 — Twin Prime Pair (2^2 × origin ± 1)

2^2 × origin − 1

2.856 × 10⁹⁶(97-digit number)

28561353274042173652…15887126312452587519

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.856 × 10⁹⁶(97-digit number)

28561353274042173652…15887126312452587521

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^2 × origin + 1 − 2^2 × origin − 1 = 2 (twin primes ✓)

Level 3 — Twin Prime Pair (2^3 × origin ± 1)

2^3 × origin − 1

5.712 × 10⁹⁶(97-digit number)

57122706548084347305…31774252624905175039

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.712 × 10⁹⁶(97-digit number)

57122706548084347305…31774252624905175041

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^3 × origin + 1 − 2^3 × origin − 1 = 2 (twin primes ✓)

Level 4 — Twin Prime Pair (2^4 × origin ± 1)

2^4 × origin − 1

1.142 × 10⁹⁷(98-digit number)

11424541309616869461…63548505249810350079

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.142 × 10⁹⁷(98-digit number)

11424541309616869461…63548505249810350081

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

Level 5 — Twin Prime Pair (2^5 × origin ± 1)

2^5 × origin − 1

2.284 × 10⁹⁷(98-digit number)

22849082619233738922…27097010499620700159

Verify on FactorDB ↗Wolfram Alpha ↗

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 — the large number shown above — anchors the chain and is divisible by a primorial (the product of small primes), cryptographically tying these prime numbers to this specific block.

★★★☆☆

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 × 3 × 5 × 7 × …), the result is the first prime in the chain. The origin is deliberately divisible by this primorial — that divisibility is part of the proof.

Prime Chain Origin = First Prime × Primorial (2·3·5·7·11·…)

Source: Primecoin prime.cpp — CheckPrimeProofOfWork()

This is why the origin has many small prime factors — 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 − 1 and p+2 = origin/primorial + 1

Cross-reference on Chainz Explorer

Block #2,647,691

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