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Block #150,361

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 9/4/2013, 11:30:12 PM Β· Difficulty 9.8590 Β· 6,657,341 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
9f70180dbe120b2c5bb34b65ee272e371804d13ebd8b112faef60bc39ac80b2f
View on Chainz β†—

Height

#150,361

Difficulty

9.858975

Transactions

1

Size

199 B

Version

2

Bits

09dbe5c8

Nonce

46,008

Timestamp

9/4/2013, 11:30:12 PM

Confirmations

6,657,341

Mined by

⛏️ P2SHAeMbsgA2smnRxpEnohyMUWwWiBqyw8TSWp

Merkle Root

c4ace6c486980f3f2782705a72f04f87b15f546ee36dbcef10d099525affd2d7
Transactions (1)
Coinbasec4ace6c486980f…d099525affd2d7
1 in β†’ 1 out10.2700 XPM109 B
AeMbsgA2…qyw8TSWp
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.

2.738 Γ— 10⁹³(94-digit number)
27380968754088402625…99486134739209759999
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
2.738 Γ— 10⁹³(94-digit number)
27380968754088402625…99486134739209759999
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.738 Γ— 10⁹³(94-digit number)
27380968754088402625…99486134739209760001
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
5.476 Γ— 10⁹³(94-digit number)
54761937508176805251…98972269478419519999
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
5.476 Γ— 10⁹³(94-digit number)
54761937508176805251…98972269478419520001
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
1.095 Γ— 10⁹⁴(95-digit number)
10952387501635361050…97944538956839039999
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.095 Γ— 10⁹⁴(95-digit number)
10952387501635361050…97944538956839040001
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
2.190 Γ— 10⁹⁴(95-digit number)
21904775003270722100…95889077913678079999
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.190 Γ— 10⁹⁴(95-digit number)
21904775003270722100…95889077913678080001
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
4.380 Γ— 10⁹⁴(95-digit number)
43809550006541444201…91778155827356159999
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:57,705,646 XPMΒ·at block #6,807,701 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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