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Block #235,416

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 10/30/2013, 9:56:31 PM Β· Difficulty 9.9457 Β· 6,566,398 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
b1b181c12c617c8088d4f6dc29d8874c7cf62c741666813fa8bc5c3af22b01f0
View on Chainz β†—

Height

#235,416

Difficulty

9.945673

Transactions

3

Size

1.36 KB

Version

2

Bits

09f2179d

Nonce

115,302

Timestamp

10/30/2013, 9:56:31 PM

Confirmations

6,566,398

Mined by

⛏️ P2SHAUm1UXE6PTt11eQB2DXhcmZJbwSTx2UrXW

Merkle Root

7ef2afbf528b3efdf18f512d852683ef7cb998633bcc98d1a23d9fb5fa9ddcfa
Transactions (3)
Coinbase1a760ca857f8c1…e05e37ce384cd9
1 in β†’ 1 out10.1100 XPM109 B
AUm1UXE6…STx2UrXW
34aeda76f5c42a…da562c41cb03dd
6 in β†’ 2 out26.4046 XPM971 B
AN7ZnJS4…uHpiPac9AKSx3UzR…6S6bEEgE
b9b7ee810d4237…c75822fb5443e9
1 in β†’ 2 out2.9571 XPM225 B
AHiwW9Qf…1mMNHnARASfPUR2t…17UGNq6r
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.

3.947 Γ— 10⁹²(93-digit number)
39471094278643655300…28480363133862353599
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
3.947 Γ— 10⁹²(93-digit number)
39471094278643655300…28480363133862353599
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
3.947 Γ— 10⁹²(93-digit number)
39471094278643655300…28480363133862353601
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
7.894 Γ— 10⁹²(93-digit number)
78942188557287310600…56960726267724707199
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
7.894 Γ— 10⁹²(93-digit number)
78942188557287310600…56960726267724707201
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
1.578 Γ— 10⁹³(94-digit number)
15788437711457462120…13921452535449414399
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.578 Γ— 10⁹³(94-digit number)
15788437711457462120…13921452535449414401
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
3.157 Γ— 10⁹³(94-digit number)
31576875422914924240…27842905070898828799
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
3.157 Γ— 10⁹³(94-digit number)
31576875422914924240…27842905070898828801
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
6.315 Γ— 10⁹³(94-digit number)
63153750845829848480…55685810141797657599
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
6.315 Γ— 10⁹³(94-digit number)
63153750845829848480…55685810141797657601
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:57,658,604 XPMΒ·at block #6,801,813 Β· updates every 60s
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