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Block #150,968

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 9/5/2013, 9:39:33 AM Β· Difficulty 9.8590 Β· 6,661,379 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
8b567ac99dc6966fb7a8f76e3c91849a508fb90b42502d4ad3f1bfbde37e342f
View on Chainz β†—

Height

#150,968

Difficulty

9.858999

Transactions

2

Size

1.90 KB

Version

2

Bits

09dbe764

Nonce

430,685

Timestamp

9/5/2013, 9:39:33 AM

Confirmations

6,661,379

Mined by

⛏️ P2SHAXAsG8Jp9YBzjDZPwVuvMsFzDf5KqHaMJo

Merkle Root

3f720a1fe5e3173247eaf6c14b6cf747dc6fe15d22c603528958ede60da8bd93
Transactions (2)
Coinbasef9254e592819d4…24fa238b520b69
1 in β†’ 1 out10.2900 XPM109 B
AXAsG8Jp…5KqHaMJo
dfcb78bd4daa75…8c22419f48f665
15 in β†’ 1 out154.9000 XPM1.71 KB
ASghs1PX…d1bLDUHV
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.

1.788 Γ— 10⁹⁸(99-digit number)
17887162653275194216…41586156782198925439
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
1.788 Γ— 10⁹⁸(99-digit number)
17887162653275194216…41586156782198925439
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.788 Γ— 10⁹⁸(99-digit number)
17887162653275194216…41586156782198925441
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
3.577 Γ— 10⁹⁸(99-digit number)
35774325306550388433…83172313564397850879
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
3.577 Γ— 10⁹⁸(99-digit number)
35774325306550388433…83172313564397850881
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
7.154 Γ— 10⁹⁸(99-digit number)
71548650613100776866…66344627128795701759
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
7.154 Γ— 10⁹⁸(99-digit number)
71548650613100776866…66344627128795701761
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
1.430 Γ— 10⁹⁹(100-digit number)
14309730122620155373…32689254257591403519
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.430 Γ— 10⁹⁹(100-digit number)
14309730122620155373…32689254257591403521
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
2.861 Γ— 10⁹⁹(100-digit number)
28619460245240310746…65378508515182807039
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:57,742,796 XPMΒ·at block #6,812,346 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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