Block #503,805

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/21/2014, 8:46:46 AM · Difficulty 10.8082 · 6,290,846 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

c1485a07a99d96f09802f4fa94a3f75ff576fd25aa71263c77c4cc9871cc9493

View on Chainz ↗

Height

#503,805

Difficulty

10.808217

Transactions

Size

870 B

Version

Bits

0acee754

Nonce

3,325

Timestamp

4/21/2014, 8:46:46 AM

Confirmations

6,290,846

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

10de8d0fbfb9f5ff067deffbf7a7ea7070adbe0b651246bb3ad0a0b8498a1930

Transactions (3)

Coinbase3d4dfc67b9a358…25bdf7bf8d35bc

1 in → 1 out8.5700 XPM110 B

AeKNrjNj…1NEq95Ta

f6d084def8cc32…4bf7480985cebc

2 in → 6 out17.1200 XPM442 B

AeKNrjNj…1NEq95Ta Ac5Sc2Mv…q4gm41o8 AQDGVS66…1PTWdWkm Abo6THXy…XGrxXxo7 AW9UAps1…PoAQ39bN

941cf6660c3d53…16321ccfa103d7

1 in → 2 out5.9869 XPM225 B

AT5KUaDs…6SrBe6Nf AdL6bbdU…YmXZXL1D

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.

1.449 × 10¹⁰²(103-digit number)

14490541623579192905…62191121179726298799

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

1.449 × 10¹⁰²(103-digit number)

14490541623579192905…62191121179726298799

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.449 × 10¹⁰²(103-digit number)

14490541623579192905…62191121179726298801

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

2.898 × 10¹⁰²(103-digit number)

28981083247158385810…24382242359452597599

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.898 × 10¹⁰²(103-digit number)

28981083247158385810…24382242359452597601

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

5.796 × 10¹⁰²(103-digit number)

57962166494316771621…48764484718905195199

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.796 × 10¹⁰²(103-digit number)

57962166494316771621…48764484718905195201

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

1.159 × 10¹⁰³(104-digit number)

11592433298863354324…97528969437810390399

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.159 × 10¹⁰³(104-digit number)

11592433298863354324…97528969437810390401

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

2.318 × 10¹⁰³(104-digit number)

23184866597726708648…95057938875620780799

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.318 × 10¹⁰³(104-digit number)

23184866597726708648…95057938875620780801

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