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Block #276,115

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 11/27/2013, 12:55:18 AM Β· Difficulty 9.9624 Β· 6,531,725 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
eb495a224fa2931585cf6aee5e089cb46cbeeb329cbd92dae06fd22a9a5cc4de
View on Chainz β†—

Height

#276,115

Difficulty

9.962391

Transactions

2

Size

389 B

Version

2

Bits

09f65f43

Nonce

150,232

Timestamp

11/27/2013, 12:55:18 AM

Confirmations

6,531,725

Mined by

⛏️ P2SHANHSimRCTXSpMVmqKWn3eBnKRFRBzv4r3d

Merkle Root

59e3463407aef1716d100a0315acc36730ba71d4039e982e39182ed58f254fca
Transactions (2)
Coinbase64750e6f8f96c3…55f61eb44ae071
1 in β†’ 1 out10.0715 XPM109 B
ANHSimRC…RBzv4r3d
cf4e63ed1d041d…9518efca8de7c3
1 in β†’ 1 out0.9900 XPM191 B
ASCWEfN3…U97E7SL2
Prime Chain Origin

This is the prime chain origin stored in the block header. It is a composite number (not prime itself) β€” it equals the first prime in the chain multiplied by a primorial. The origin anchors the entire chain to this specific block.

8.707 Γ— 10⁹²(93-digit number)
87073913620440685726…03953238645771647999
Discovered Prime Numbers
Lower: 2^k Γ— origin βˆ’ 1 | Upper: 2^k Γ— 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 β€” Twin Prime Pair (origin Β± 1)
origin βˆ’ 1
8.707 Γ— 10⁹²(93-digit number)
87073913620440685726…03953238645771647999
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
8.707 Γ— 10⁹²(93-digit number)
87073913620440685726…03953238645771648001
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: origin + 1 βˆ’ origin βˆ’ 1 = 2 (twin primes βœ“)
Level 1 β€” Twin Prime Pair (2^1 Γ— origin Β± 1)
2^1 Γ— origin βˆ’ 1
1.741 Γ— 10⁹³(94-digit number)
17414782724088137145…07906477291543295999
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.741 Γ— 10⁹³(94-digit number)
17414782724088137145…07906477291543296001
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^1 Γ— origin + 1 βˆ’ 2^1 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 2 β€” Twin Prime Pair (2^2 Γ— origin Β± 1)
2^2 Γ— origin βˆ’ 1
3.482 Γ— 10⁹³(94-digit number)
34829565448176274290…15812954583086591999
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
3.482 Γ— 10⁹³(94-digit number)
34829565448176274290…15812954583086592001
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^2 Γ— origin + 1 βˆ’ 2^2 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 3 β€” Twin Prime Pair (2^3 Γ— origin Β± 1)
2^3 Γ— origin βˆ’ 1
6.965 Γ— 10⁹³(94-digit number)
69659130896352548581…31625909166173183999
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
6.965 Γ— 10⁹³(94-digit number)
69659130896352548581…31625909166173184001
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^3 Γ— origin + 1 βˆ’ 2^3 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 4 β€” Twin Prime Pair (2^4 Γ— origin Β± 1)
2^4 Γ— origin βˆ’ 1
1.393 Γ— 10⁹⁴(95-digit number)
13931826179270509716…63251818332346367999
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.393 Γ— 10⁹⁴(95-digit number)
13931826179270509716…63251818332346368001
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^4 Γ— origin + 1 βˆ’ 2^4 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)

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 β€” the large number shown above β€” anchors the chain and is divisible by a primorial (the product of small primes), cryptographically tying these prime numbers to this specific block.

β˜…β˜…β˜†β˜†β˜†
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 Γ— 3 Γ— 5 Γ— 7 Γ— …), the result is the first prime in the chain. The origin is deliberately divisible by this primorial β€” that divisibility is part of the proof.

Prime Chain Origin = First Prime Γ— Primorial (2Β·3Β·5Β·7Β·11·…)
Source: Primecoin prime.cpp β€” CheckPrimeProofOfWork()

This is why the origin has many small prime factors β€” 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 βˆ’ 1 and p+2 = origin/primorial + 1
Cross-reference on Chainz Explorer
Circulating Supply:57,706,758 XPMΒ·at block #6,807,839 Β· updates every 60s
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