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Block #236,061

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 10/31/2013, 7:11:37 AM Β· Difficulty 9.9467 Β· 6,559,462 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
5209e6d21d6319418e54f46d57b4ddf39dc83f9c8d659bc076548c5511471747
View on Chainz β†—

Height

#236,061

Difficulty

9.946651

Transactions

1

Size

198 B

Version

2

Bits

09f257b2

Nonce

66,897

Timestamp

10/31/2013, 7:11:37 AM

Confirmations

6,559,462

Mined by

⛏️ P2SHAQ4KuZ2UkkCs8rHce3kHkL7Wmf1UKD59gi

Merkle Root

0281d270b6139e36b9951104ae2e3401851e3ba8e3d71784eb25c87b3370068f
Transactions (1)
Coinbase0281d270b6139e…25c87b3370068f
1 in β†’ 1 out10.0900 XPM109 B
AQ4KuZ2U…1UKD59gi
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.

1.601 Γ— 10⁹³(94-digit number)
16010830655884873419…92133940373475362099
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
1.601 Γ— 10⁹³(94-digit number)
16010830655884873419…92133940373475362099
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.601 Γ— 10⁹³(94-digit number)
16010830655884873419…92133940373475362101
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
3.202 Γ— 10⁹³(94-digit number)
32021661311769746838…84267880746950724199
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
3.202 Γ— 10⁹³(94-digit number)
32021661311769746838…84267880746950724201
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
6.404 Γ— 10⁹³(94-digit number)
64043322623539493676…68535761493901448399
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
6.404 Γ— 10⁹³(94-digit number)
64043322623539493676…68535761493901448401
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
1.280 Γ— 10⁹⁴(95-digit number)
12808664524707898735…37071522987802896799
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.280 Γ— 10⁹⁴(95-digit number)
12808664524707898735…37071522987802896801
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
2.561 Γ— 10⁹⁴(95-digit number)
25617329049415797470…74143045975605793599
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
2.561 Γ— 10⁹⁴(95-digit number)
25617329049415797470…74143045975605793601
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:57,608,246 XPMΒ·at block #6,795,522 Β· updates every 60s
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