Block #603,386

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 6/27/2014, 12:35:12 AM · Difficulty 10.9117 · 6,205,850 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

0934140ca7cdf172d616d091fd3b5c25a2087974e801f464221a85f55900cbbd

View on Chainz ↗

Height

#603,386

Difficulty

10.911695

Transactions

Size

810 B

Version

Bits

0ae964d8

Nonce

94,714,424

Timestamp

6/27/2014, 12:35:12 AM

Confirmations

6,205,850

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

435fb5077f33b6f8d141408127d7bd9d5b4a2a39ece518e16e9aed5248db134a

Transactions (3)

Coinbasefa02b90eb45493…d883c66e875cde

1 in → 1 out8.4100 XPM116 B

ANSXnLY2…Sd25TjkD

75944b50a92f85…c8c221e01dad85

2 in → 2 out10.6864 XPM375 B

AJobsSzq…SoqYjNSw AdD5Hdbr…ovRgosLc

7530d42d4bf41a…0cf17bf9be4d64

1 in → 2 out5.9426 XPM226 B

Abs1CTRR…uk6ieBYF AGS37PdC…V89f9qPU

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.

1.799 × 10¹⁰¹(102-digit number)

17997041121121944662…64602153532854763519

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

1.799 × 10¹⁰¹(102-digit number)

17997041121121944662…64602153532854763519

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.799 × 10¹⁰¹(102-digit number)

17997041121121944662…64602153532854763521

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

3.599 × 10¹⁰¹(102-digit number)

35994082242243889325…29204307065709527039

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.599 × 10¹⁰¹(102-digit number)

35994082242243889325…29204307065709527041

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

7.198 × 10¹⁰¹(102-digit number)

71988164484487778650…58408614131419054079

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

7.198 × 10¹⁰¹(102-digit number)

71988164484487778650…58408614131419054081

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

1.439 × 10¹⁰²(103-digit number)

14397632896897555730…16817228262838108159

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.439 × 10¹⁰²(103-digit number)

14397632896897555730…16817228262838108161

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

2.879 × 10¹⁰²(103-digit number)

28795265793795111460…33634456525676216319

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.879 × 10¹⁰²(103-digit number)

28795265793795111460…33634456525676216321

Verify on FactorDB ↗Wolfram Alpha ↗

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

What this block proved

The miner who found this block proved the existence of 10 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

UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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 #603,386

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