Block #59,672

TWNLength 8★☆☆☆☆

Bi-Twin Chain · Discovered 7/18/2013, 3:38:58 AM · Difficulty 8.9659 · 6,755,302 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

fe3b3473563c182ffacc6153b3335e9b9a57088b0a1dfe9373b44211e2792524

View on Chainz ↗

Height

#59,672

Difficulty

8.965934

Transactions

Size

1.48 KB

Version

Bits

08f74772

Nonce

Timestamp

7/18/2013, 3:38:58 AM

Confirmations

6,755,302

Mined by

⛏️ P2SHALAKWqBr5hqzeg72yRoodDyrbCjvMnhUct

Merkle Root

a2f2278cc67ed27ea357f9fbe0410ed088822e095197855cd53692c10f69a6d5

Transactions (4)

Coinbase02f3139dc5cea6…36ee3c6c27edba

1 in → 1 out12.4500 XPM109 B

ALAKWqBr…jvMnhUct

77104bf373bc6e…71d58648ee74bb

3 in → 1 out40.6000 XPM384 B

AZjAawhu…JwrCuhga

71be13b3c849a4…6e09a0b141c444

3 in → 2 out6.0018 XPM520 B

AK9zkvFC…gVk2XcDN AKMLwtxE…Et9DYCu7

2caf88b703230e…6120d8868e995f

2 in → 3 out5.1200 XPM407 B

AWcZjGw7…FWC6X8Wu ANUGXYx2…QoaEhmZm AH3vj8Mr…Zh4arJbh

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.

2.004 × 10¹¹⁰(111-digit number)

20049525427398259325…16132922175577065839

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

2.004 × 10¹¹⁰(111-digit number)

20049525427398259325…16132922175577065839

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.004 × 10¹¹⁰(111-digit number)

20049525427398259325…16132922175577065841

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

4.009 × 10¹¹⁰(111-digit number)

40099050854796518650…32265844351154131679

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.009 × 10¹¹⁰(111-digit number)

40099050854796518650…32265844351154131681

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

8.019 × 10¹¹⁰(111-digit number)

80198101709593037300…64531688702308263359

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

8.019 × 10¹¹⁰(111-digit number)

80198101709593037300…64531688702308263361

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

1.603 × 10¹¹¹(112-digit number)

16039620341918607460…29063377404616526719

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.603 × 10¹¹¹(112-digit number)

16039620341918607460…29063377404616526721

Verify on FactorDB ↗Wolfram Alpha ↗

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

What this block proved

The miner who found this block proved the existence of 8 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

CommonChain length 8

Found in most blocks. The baseline for Primecoin's proof-of-work.

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 #59,672

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