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Block #60,427

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 7/18/2013, 7:52:16 AM Β· Difficulty 8.9692 Β· 6,745,382 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
ec395f9a005bc9156638b2f0abe0c6edbc46af298334ef19efbc87881476fd34
View on Chainz β†—

Height

#60,427

Difficulty

8.969182

Transactions

1

Size

201 B

Version

2

Bits

08f81c49

Nonce

1,681

Timestamp

7/18/2013, 7:52:16 AM

Confirmations

6,745,382

Mined by

⛏️ P2SHAKsLKPc8KMAFsNueJDJSs3dfp1zkBgUqcr

Merkle Root

8c5ec8172dd4a6d53d8c39f47e0e0db55927a3a8f73d6328c3ecae564e6efaec
Transactions (1)
Coinbase8c5ec8172dd4a6…ecae564e6efaec
1 in β†’ 1 out12.4100 XPM110 B
AKsLKPc8…zkBgUqcr
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.

4.002 Γ— 10⁹⁢(97-digit number)
40029278077472530749…29325816155955648139
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
4.002 Γ— 10⁹⁢(97-digit number)
40029278077472530749…29325816155955648139
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
4.002 Γ— 10⁹⁢(97-digit number)
40029278077472530749…29325816155955648141
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
8.005 Γ— 10⁹⁢(97-digit number)
80058556154945061499…58651632311911296279
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
8.005 Γ— 10⁹⁢(97-digit number)
80058556154945061499…58651632311911296281
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
1.601 Γ— 10⁹⁷(98-digit number)
16011711230989012299…17303264623822592559
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.601 Γ— 10⁹⁷(98-digit number)
16011711230989012299…17303264623822592561
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
3.202 Γ— 10⁹⁷(98-digit number)
32023422461978024599…34606529247645185119
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
3.202 Γ— 10⁹⁷(98-digit number)
32023422461978024599…34606529247645185121
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
6.404 Γ— 10⁹⁷(98-digit number)
64046844923956049199…69213058495290370239
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:57,690,557 XPMΒ·at block #6,805,808 Β· updates every 60s
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