Block #208,537

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 10/14/2013, 1:34:12 AM · Difficulty 9.9069 · 6,599,460 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

f8b53a4236404b8bf8e51798a540fc1552d0bcdfcff3457a82f721606337557c

View on Chainz ↗

Height

#208,537

Difficulty

9.906855

Transactions

Size

9.46 KB

Version

Bits

09e827a4

Nonce

2,342

Timestamp

10/14/2013, 1:34:12 AM

Confirmations

6,599,460

Mined by

⛏️ P2SHAGEGbgd2eoANsp1E5VNPQue4HVk4nQrXdo

Merkle Root

3fd7ca47d7e25649ee72574ade1ff0129ba800bd03b5bbbafb5d1369e0871f79

Transactions (5)

Coinbase1fedc022792ef3…1422bbc8448e0e

1 in → 1 out10.2900 XPM109 B

AGEGbgd2…k4nQrXdo

7b73a644d74532…985dee53d5c7b1

1 in → 2 out50.9036 XPM227 B

AQMD1jUX…CJt3eBQq AL9QYT6h…EExU8BRE

63e37181364e95…9f2b5050fb4008

73 in → 1 out750.0000 XPM8.17 KB

AGEBmx77…rXF6mZuA

418f7ed1771d97…b40207a26a0240

3 in → 2 out26.1367 XPM523 B

APeNDkSF…jT4mfzb1 ASuoUi24…FwBoFbxd

648fb6913a4563…a269740136dd06

2 in → 2 out19.6152 XPM375 B

AYzHMeqY…bbJxsWbk AHyHEeYQ…XuELsExj

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.

2.226 × 10⁸⁹(90-digit number)

22264243473281497794…01564256992672955719

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

2.226 × 10⁸⁹(90-digit number)

22264243473281497794…01564256992672955719

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.226 × 10⁸⁹(90-digit number)

22264243473281497794…01564256992672955721

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

4.452 × 10⁸⁹(90-digit number)

44528486946562995588…03128513985345911439

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.452 × 10⁸⁹(90-digit number)

44528486946562995588…03128513985345911441

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

8.905 × 10⁸⁹(90-digit number)

89056973893125991177…06257027970691822879

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

8.905 × 10⁸⁹(90-digit number)

89056973893125991177…06257027970691822881

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

1.781 × 10⁹⁰(91-digit number)

17811394778625198235…12514055941383645759

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.781 × 10⁹⁰(91-digit number)

17811394778625198235…12514055941383645761

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

3.562 × 10⁹⁰(91-digit number)

35622789557250396470…25028111882767291519

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 9 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

CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

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 #208,537

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