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Block #1,527,686

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 4/5/2016, 3:11:59 PM Β· Difficulty 10.6082 Β· 5,289,944 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
c7fb3d8fa9a463030932be2003bf51cc44f5ddbd03786587b2e5544fdc7dd2e0
View on Chainz β†—

Height

#1,527,686

Difficulty

10.608227

Transactions

2

Size

8.80 KB

Version

2

Bits

0a9bb4c7

Nonce

606,155,479

Timestamp

4/5/2016, 3:11:59 PM

Confirmations

5,289,944

Mined by

⛏️ P2SHAXHcU1YgxozYAz68zPaKshm47HMRsMEkUF

Merkle Root

16c0d6b8ae172f0163da241723d215937f2d509d1725fa546c3555ce27bad24a
Transactions (2)
Coinbasee68134f1d539e5…a1c78607f1e27f
1 in β†’ 1 out8.9700 XPM109 B
AXHcU1Yg…MRsMEkUF
623db21f2fb9b5…2f0eeef49a4cfa
59 in β†’ 2 out7.1100 XPM8.60 KB
AW9z6iyE…ZMok5rfxAKfr5T7X…239WW6mt
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.

1.916 Γ— 10⁹⁢(97-digit number)
19165569825826620964…21340067903160934399
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
1.916 Γ— 10⁹⁢(97-digit number)
19165569825826620964…21340067903160934399
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.916 Γ— 10⁹⁢(97-digit number)
19165569825826620964…21340067903160934401
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
3.833 Γ— 10⁹⁢(97-digit number)
38331139651653241929…42680135806321868799
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
3.833 Γ— 10⁹⁢(97-digit number)
38331139651653241929…42680135806321868801
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
7.666 Γ— 10⁹⁢(97-digit number)
76662279303306483858…85360271612643737599
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
7.666 Γ— 10⁹⁢(97-digit number)
76662279303306483858…85360271612643737601
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
1.533 Γ— 10⁹⁷(98-digit number)
15332455860661296771…70720543225287475199
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.533 Γ— 10⁹⁷(98-digit number)
15332455860661296771…70720543225287475201
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
3.066 Γ— 10⁹⁷(98-digit number)
30664911721322593543…41441086450574950399
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
3.066 Γ— 10⁹⁷(98-digit number)
30664911721322593543…41441086450574950401
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:57,785,092 XPMΒ·at block #6,817,629 Β· updates every 60s
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