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Block #539,789

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 5/12/2014, 9:06:38 PM Β· Difficulty 10.9299 Β· 6,287,058 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
6c20fa53599d10d055a30942adedcb58b4973f2cec7dca312e6cf1843150cd5c
View on Chainz β†—

Height

#539,789

Difficulty

10.929919

Transactions

1

Size

207 B

Version

2

Bits

0aee0f33

Nonce

65,160,839

Timestamp

5/12/2014, 9:06:38 PM

Confirmations

6,287,058

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

295ee42323a1d135aebd71a23333a13760854e6d19e827a0a2a70d40236aaaca
Transactions (1)
Coinbase295ee42323a1d1…a70d40236aaaca
1 in β†’ 1 out8.3600 XPM116 B
ANSXnLY2…Sd25TjkD
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.

1.618 Γ— 10⁹⁸(99-digit number)
16181456985972385856…51028363942754140159
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
1.618 Γ— 10⁹⁸(99-digit number)
16181456985972385856…51028363942754140159
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.618 Γ— 10⁹⁸(99-digit number)
16181456985972385856…51028363942754140161
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
3.236 Γ— 10⁹⁸(99-digit number)
32362913971944771713…02056727885508280319
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
3.236 Γ— 10⁹⁸(99-digit number)
32362913971944771713…02056727885508280321
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
6.472 Γ— 10⁹⁸(99-digit number)
64725827943889543426…04113455771016560639
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
6.472 Γ— 10⁹⁸(99-digit number)
64725827943889543426…04113455771016560641
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
1.294 Γ— 10⁹⁹(100-digit number)
12945165588777908685…08226911542033121279
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.294 Γ— 10⁹⁹(100-digit number)
12945165588777908685…08226911542033121281
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
2.589 Γ— 10⁹⁹(100-digit number)
25890331177555817370…16453823084066242559
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
2.589 Γ— 10⁹⁹(100-digit number)
25890331177555817370…16453823084066242561
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^4 Γ— origin + 1 βˆ’ 2^4 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)

What this block proved

The miner who found this block proved the existence of 10 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
UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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:57,858,942 XPMΒ·at block #6,826,846 Β· updates every 60s
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