Block #638,774

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 7/18/2014, 7:52:02 PM · Difficulty 10.9609 · 6,165,288 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

4e38ac803336974e47df447f881d31b32fe10afa4aff4e74fce1f08e1af5f6d3

View on Chainz ↗

Height

#638,774

Difficulty

10.960926

Transactions

Size

2.17 KB

Version

Bits

0af5ff45

Nonce

756,056,660

Timestamp

7/18/2014, 7:52:02 PM

Confirmations

6,165,288

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

f2c023e0dcad158442418f08c7f3dfe926e1cc55e23956ab8968650b4600b973

Transactions (4)

Coinbase4b32185b79b6e1…26971513d37a3c

1 in → 1 out8.3400 XPM116 B

ANSXnLY2…Sd25TjkD

4817f21db44363…c4eb64adb00bd2

6 in → 2 out23.5351 XPM968 B

AZazk8Si…VLN9QhrU APUCisBU…QCP13amA

c7cf447fcf9635…1a6a6fe12bef1d

2 in → 2 out10.9546 XPM374 B

ATCXp9Qh…Jt5sAAon AJzjuYh3…ndhqFVng

d2a16e4698e580…38d78a4d9d7a0f

4 in → 2 out10.0694 XPM669 B

AUgdNbLS…8twAgHic ARycPRm4…pN32Ppkf

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.

4.725 × 10⁹⁸(99-digit number)

47252825471155462187…13479249744426598399

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

4.725 × 10⁹⁸(99-digit number)

47252825471155462187…13479249744426598399

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.725 × 10⁹⁸(99-digit number)

47252825471155462187…13479249744426598401

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

9.450 × 10⁹⁸(99-digit number)

94505650942310924375…26958499488853196799

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

9.450 × 10⁹⁸(99-digit number)

94505650942310924375…26958499488853196801

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

1.890 × 10⁹⁹(100-digit number)

18901130188462184875…53916998977706393599

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.890 × 10⁹⁹(100-digit number)

18901130188462184875…53916998977706393601

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

3.780 × 10⁹⁹(100-digit number)

37802260376924369750…07833997955412787199

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.780 × 10⁹⁹(100-digit number)

37802260376924369750…07833997955412787201

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

7.560 × 10⁹⁹(100-digit number)

75604520753848739500…15667995910825574399

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

7.560 × 10⁹⁹(100-digit number)

75604520753848739500…15667995910825574401

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

1.512 × 10¹⁰⁰(101-digit number)

15120904150769747900…31335991821651148799

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