Block #636,271

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 7/16/2014, 7:23:03 PM · Difficulty 10.9639 · 6,181,569 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

6e62792658afe07c60c07590e606f784ea4cb72b15c909449cdaa4a49b45e0f4

View on Chainz ↗

Height

#636,271

Difficulty

10.963886

Transactions

Size

1.81 KB

Version

Bits

0af6c13d

Nonce

759,693,813

Timestamp

7/16/2014, 7:23:03 PM

Confirmations

6,181,569

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

33a7b30b400817c7d357f8ed27d2bc8293c94528bc524614e0cb56bf1f7d190a

Transactions (5)

Coinbaseba247968e602af…965fcbd9c7d85a

1 in → 1 out8.3500 XPM116 B

ANSXnLY2…Sd25TjkD

8e36d5e0824f95…1373a20d5cfffc

1 in → 2 out6.2521 XPM227 B

ARnTzB35…gUXRz9Fw ATPNVTZF…yexnRmNw

8cb1c3be35f4ef…ca8c74c5b93b73

1 in → 2 out6.1193 XPM225 B

Ab5NWMK7…UiQCVjiw AS9ZCvju…bu3NEFwZ

0e3a8d3f28dec2…4914a0942e0177

1 in → 2 out4.2602 XPM226 B

AW8TPY8D…BxhKtRbM Ab3ZA77H…R7ktRp2N

221f7ff0d09da8…0d0f335c545b73

6 in → 2 out1.0156 XPM967 B

APdxEFcn…vLJMcBEX AZpdkvSw…MADC6brT

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.

6.075 × 10⁹⁸(99-digit number)

60758340010872170460…72062328278118399999

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

6.075 × 10⁹⁸(99-digit number)

60758340010872170460…72062328278118399999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

6.075 × 10⁹⁸(99-digit number)

60758340010872170460…72062328278118400001

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

1.215 × 10⁹⁹(100-digit number)

12151668002174434092…44124656556236799999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.215 × 10⁹⁹(100-digit number)

12151668002174434092…44124656556236800001

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

2.430 × 10⁹⁹(100-digit number)

24303336004348868184…88249313112473599999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.430 × 10⁹⁹(100-digit number)

24303336004348868184…88249313112473600001

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

4.860 × 10⁹⁹(100-digit number)

48606672008697736368…76498626224947199999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.860 × 10⁹⁹(100-digit number)

48606672008697736368…76498626224947200001

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

9.721 × 10⁹⁹(100-digit number)

97213344017395472736…52997252449894399999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

9.721 × 10⁹⁹(100-digit number)

97213344017395472736…52997252449894400001

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 #636,271

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