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Block #1,478,068

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 3/1/2016, 3:13:05 AM Β· Difficulty 10.7076 Β· 5,364,396 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
76164c5a5e49f8a20ffeea23844eefe3a50d84ef6f4dfc7c7532639488eccb6a
View on Chainz β†—

Height

#1,478,068

Difficulty

10.707583

Transactions

1

Size

242 B

Version

2

Bits

0ab5242e

Nonce

753,021,022

Timestamp

3/1/2016, 3:13:05 AM

Confirmations

5,364,396

Mined by

⛏️ P2SHAdwKJkgSub5gUckyBUnSUJCm23L2zsc2ej

Merkle Root

86694509f5cd12989798e8e784523ec7d1d541fa7c98a662e6b9fdf18400fec8
Transactions (1)
Coinbase86694509f5cd12…b9fdf18400fec8
1 in β†’ 2 out8.7100 XPM152 B
AdwKJkgS…L2zsc2ejALPu3s2c…EJXLjVFh
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.

4.829 Γ— 10⁹³(94-digit number)
48295791292353076221…66034099268659773759
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
4.829 Γ— 10⁹³(94-digit number)
48295791292353076221…66034099268659773759
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
4.829 Γ— 10⁹³(94-digit number)
48295791292353076221…66034099268659773761
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
9.659 Γ— 10⁹³(94-digit number)
96591582584706152442…32068198537319547519
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
9.659 Γ— 10⁹³(94-digit number)
96591582584706152442…32068198537319547521
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
1.931 Γ— 10⁹⁴(95-digit number)
19318316516941230488…64136397074639095039
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.931 Γ— 10⁹⁴(95-digit number)
19318316516941230488…64136397074639095041
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
3.863 Γ— 10⁹⁴(95-digit number)
38636633033882460977…28272794149278190079
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
3.863 Γ— 10⁹⁴(95-digit number)
38636633033882460977…28272794149278190081
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
7.727 Γ— 10⁹⁴(95-digit number)
77273266067764921954…56545588298556380159
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
7.727 Γ— 10⁹⁴(95-digit number)
77273266067764921954…56545588298556380161
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:57,984,130 XPMΒ·at block #6,842,463 Β· updates every 60s
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