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Block #30,090

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 7/13/2013, 5:48:42 PM Β· Difficulty 7.9861 Β· 6,772,929 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
05ecdbe880b3ad73da826d0642e38e6fdda6672cb1735af26c03adb925aaeef8
View on Chainz β†—

Height

#30,090

Difficulty

7.986135

Transactions

2

Size

392 B

Version

2

Bits

07fc7357

Nonce

567

Timestamp

7/13/2013, 5:48:42 PM

Confirmations

6,772,929

Mined by

⛏️ P2SHAcd84YfnJ22yfPwV4CfhQ7bTiVcXp6gwCP

Merkle Root

6a0d1622a9ccc890936dc33fc3d84ef537cf72f75619e54f570ddfec7143d0a6
Transactions (2)
Coinbasefc171b82b6157b…a452679577a70e
1 in β†’ 1 out15.6700 XPM108 B
Acd84Yfn…cXp6gwCP
d7a86a0b0ce044…84c94c7fb2460d
1 in β†’ 1 out249.9900 XPM192 B
AYdGorU2…mUwWxCte
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.

5.778 Γ— 10⁹⁹(100-digit number)
57784433937823454753…05872164192229316149
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
5.778 Γ— 10⁹⁹(100-digit number)
57784433937823454753…05872164192229316149
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
5.778 Γ— 10⁹⁹(100-digit number)
57784433937823454753…05872164192229316151
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
1.155 Γ— 10¹⁰⁰(101-digit number)
11556886787564690950…11744328384458632299
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.155 Γ— 10¹⁰⁰(101-digit number)
11556886787564690950…11744328384458632301
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
2.311 Γ— 10¹⁰⁰(101-digit number)
23113773575129381901…23488656768917264599
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.311 Γ— 10¹⁰⁰(101-digit number)
23113773575129381901…23488656768917264601
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
4.622 Γ— 10¹⁰⁰(101-digit number)
46227547150258763803…46977313537834529199
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
4.622 Γ— 10¹⁰⁰(101-digit number)
46227547150258763803…46977313537834529201
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
9.245 Γ— 10¹⁰⁰(101-digit number)
92455094300517527606…93954627075669058399
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:57,668,182 XPMΒ·at block #6,803,018 Β· updates every 60s
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