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Block #154,959

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 9/8/2013, 12:31:36 AM Β· Difficulty 9.8651 Β· 6,649,968 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
bc30e3181478c699d1e8c4943db88202769f6482f8c763fa7f2740088f13e8e1
View on Chainz β†—

Height

#154,959

Difficulty

9.865071

Transactions

1

Size

198 B

Version

2

Bits

09dd7548

Nonce

77,382

Timestamp

9/8/2013, 12:31:36 AM

Confirmations

6,649,968

Mined by

⛏️ P2SHAQE5juVGf2GjfXcDEExb1YTp8cv2LcRcDH

Merkle Root

036aca5c7314f5f52b10520f0ac9d9936222f9a44d96cdbd08b327085b4831a1
Transactions (1)
Coinbase036aca5c7314f5…b327085b4831a1
1 in β†’ 1 out10.2600 XPM109 B
AQE5juVG…v2LcRcDH
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.

1.158 Γ— 10⁹²(93-digit number)
11588702109881511517…14818054090727639039
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
1.158 Γ— 10⁹²(93-digit number)
11588702109881511517…14818054090727639039
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.158 Γ— 10⁹²(93-digit number)
11588702109881511517…14818054090727639041
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
2.317 Γ— 10⁹²(93-digit number)
23177404219763023034…29636108181455278079
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.317 Γ— 10⁹²(93-digit number)
23177404219763023034…29636108181455278081
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
4.635 Γ— 10⁹²(93-digit number)
46354808439526046068…59272216362910556159
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
4.635 Γ— 10⁹²(93-digit number)
46354808439526046068…59272216362910556161
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
9.270 Γ— 10⁹²(93-digit number)
92709616879052092136…18544432725821112319
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
9.270 Γ— 10⁹²(93-digit number)
92709616879052092136…18544432725821112321
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
1.854 Γ— 10⁹³(94-digit number)
18541923375810418427…37088865451642224639
Verify on FactorDB β†—Wolfram Alpha β†—

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 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
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 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:57,683,490 XPMΒ·at block #6,804,926 Β· updates every 60s
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