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Block #933,064

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 2/12/2015, 9:16:39 AM Β· Difficulty 10.9022 Β· 5,892,234 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
bd5e6aecdabeda5f41263ddcb22d9ea2ae99645d24639dd7458cd85b011462bf
View on Chainz β†—

Height

#933,064

Difficulty

10.902186

Transactions

2

Size

472 B

Version

2

Bits

0ae6f5ab

Nonce

153,720,057

Timestamp

2/12/2015, 9:16:39 AM

Confirmations

5,892,234

Mined by

⛏️ P2SHAYgUuX2nvACTUaJedSgCzev66HYpWrouXx

Merkle Root

71acf396ef90981ab162c0119c373b891de49db4cd55115c9170d75e44cf37a7
Transactions (2)
Coinbase9347e6791781ee…6a1727eba4a27f
1 in β†’ 1 out8.4100 XPM110 B
AYgUuX2n…YpWrouXx
4334c33972f649…6c744df47fcf23
2 in β†’ 1 out16.7900 XPM271 B
AekLq4Sw…ueWMfyir
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.

1.398 Γ— 10⁹⁢(97-digit number)
13984598640683541819…84605499239518131199
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
1.398 Γ— 10⁹⁢(97-digit number)
13984598640683541819…84605499239518131199
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.398 Γ— 10⁹⁢(97-digit number)
13984598640683541819…84605499239518131201
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
2.796 Γ— 10⁹⁢(97-digit number)
27969197281367083639…69210998479036262399
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.796 Γ— 10⁹⁢(97-digit number)
27969197281367083639…69210998479036262401
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
5.593 Γ— 10⁹⁢(97-digit number)
55938394562734167279…38421996958072524799
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
5.593 Γ— 10⁹⁢(97-digit number)
55938394562734167279…38421996958072524801
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
1.118 Γ— 10⁹⁷(98-digit number)
11187678912546833455…76843993916145049599
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.118 Γ— 10⁹⁷(98-digit number)
11187678912546833455…76843993916145049601
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
2.237 Γ— 10⁹⁷(98-digit number)
22375357825093666911…53687987832290099199
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
2.237 Γ— 10⁹⁷(98-digit number)
22375357825093666911…53687987832290099201
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:57,846,485 XPMΒ·at block #6,825,297 Β· updates every 60s
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