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Block #487,460

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 4/12/2014, 4:04:49 AM Β· Difficulty 10.6410 Β· 6,318,780 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
3ce148cc3c6fbc866607b0c94bcd13bd55fd3dfee990115d55e429482fe3e0e5
View on Chainz β†—

Height

#487,460

Difficulty

10.641004

Transactions

2

Size

542 B

Version

2

Bits

0aa418d8

Nonce

183,341,775

Timestamp

4/12/2014, 4:04:49 AM

Confirmations

6,318,780

Mined by

⛏️ P2SHAXuF5m5zstut6r1qVa8XfBT45VxSZ42JSU

Merkle Root

5d218a887ea82200a7370ee208f3b93019ce086b578e6372682d6e2a5e753884
Transactions (2)
Coinbase8726333fbd8495…85dfcd8e1198b8
1 in β†’ 1 out8.8300 XPM111 B
AXuF5m5z…xSZ42JSU
fc36d8698b04ea…4771c7693d3fb1
2 in β†’ 1 out54.9900 XPM339 B
ARqLqg7j…tcvtkFxP
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.

2.418 Γ— 10⁹⁹(100-digit number)
24181125347968550268…79881646672658872319
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
2.418 Γ— 10⁹⁹(100-digit number)
24181125347968550268…79881646672658872319
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.418 Γ— 10⁹⁹(100-digit number)
24181125347968550268…79881646672658872321
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
4.836 Γ— 10⁹⁹(100-digit number)
48362250695937100537…59763293345317744639
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
4.836 Γ— 10⁹⁹(100-digit number)
48362250695937100537…59763293345317744641
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
9.672 Γ— 10⁹⁹(100-digit number)
96724501391874201074…19526586690635489279
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
9.672 Γ— 10⁹⁹(100-digit number)
96724501391874201074…19526586690635489281
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
1.934 Γ— 10¹⁰⁰(101-digit number)
19344900278374840214…39053173381270978559
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.934 Γ— 10¹⁰⁰(101-digit number)
19344900278374840214…39053173381270978561
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
3.868 Γ— 10¹⁰⁰(101-digit number)
38689800556749680429…78106346762541957119
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
3.868 Γ— 10¹⁰⁰(101-digit number)
38689800556749680429…78106346762541957121
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:57,694,001 XPMΒ·at block #6,806,239 Β· updates every 60s
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