Block #624,064

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 7/8/2014, 8:32:40 PM · Difficulty 10.9576 · 6,201,117 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

e0b928666502bdc773fc30a3e5872ff4461856a97dcb2fd33178a935adee8078

View on Chainz ↗

Height

#624,064

Difficulty

10.957602

Transactions

Size

2.64 KB

Version

Bits

0af5256d

Nonce

2,174,239,404

Timestamp

7/8/2014, 8:32:40 PM

Confirmations

6,201,117

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

1b41587f2730381b2b24acc5bb7e520e2c6c3d8956bbd851e43d8ae1e40e9190

Transactions (3)

Coinbase009806c9bd80cf…9cf5d1e0b0621c

1 in → 1 out8.3600 XPM116 B

ANSXnLY2…Sd25TjkD

2225613593f01d…46ef6b9d83f706

1 in → 2 out8.3200 XPM227 B

AVQG7b2g…FkVhY2sy AMcRrTzr…uYaFHvtp

4140a20135338d…ced8eab75d1827

15 in → 1 out44.2025 XPM2.21 KB

AeUK68Bs…2MGVKpR2

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.

1.507 × 10⁹⁹(100-digit number)

15075807439183850818…31640573792145735679

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

1.507 × 10⁹⁹(100-digit number)

15075807439183850818…31640573792145735679

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.507 × 10⁹⁹(100-digit number)

15075807439183850818…31640573792145735681

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

3.015 × 10⁹⁹(100-digit number)

30151614878367701637…63281147584291471359

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.015 × 10⁹⁹(100-digit number)

30151614878367701637…63281147584291471361

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

6.030 × 10⁹⁹(100-digit number)

60303229756735403274…26562295168582942719

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

6.030 × 10⁹⁹(100-digit number)

60303229756735403274…26562295168582942721

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

1.206 × 10¹⁰⁰(101-digit number)

12060645951347080654…53124590337165885439

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.206 × 10¹⁰⁰(101-digit number)

12060645951347080654…53124590337165885441

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

2.412 × 10¹⁰⁰(101-digit number)

24121291902694161309…06249180674331770879

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.412 × 10¹⁰⁰(101-digit number)

24121291902694161309…06249180674331770881

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 #624,064

Cookie Preferences