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Block #74,610

TWNLength 8β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 7/21/2013, 12:02:25 PM Β· Difficulty 8.9956 Β· 6,719,845 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
c5888a2b2b9e4d1425464510a42d506fed31bb1e6edb514d5511c0bbd0b3af95
View on Chainz β†—

Height

#74,610

Difficulty

8.995615

Transactions

1

Size

202 B

Version

2

Bits

08fee09f

Nonce

264

Timestamp

7/21/2013, 12:02:25 PM

Confirmations

6,719,845

Mined by

⛏️ P2SHAVQxbFsH6aZpX2pFKM69EEQVEFKG2vYXbz

Merkle Root

3a39586c62e73661a77e3946423d4c5d99bdc2eaf6f6a890e1f82e05e8b655bc
Transactions (1)
Coinbase3a39586c62e736…f82e05e8b655bc
1 in β†’ 1 out12.3400 XPM110 B
AVQxbFsH…KG2vYXbz
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.

1.613 Γ— 10¹⁰⁰(101-digit number)
16135274077038170342…62712420001511138799
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
1.613 Γ— 10¹⁰⁰(101-digit number)
16135274077038170342…62712420001511138799
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.613 Γ— 10¹⁰⁰(101-digit number)
16135274077038170342…62712420001511138801
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
3.227 Γ— 10¹⁰⁰(101-digit number)
32270548154076340684…25424840003022277599
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
3.227 Γ— 10¹⁰⁰(101-digit number)
32270548154076340684…25424840003022277601
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
6.454 Γ— 10¹⁰⁰(101-digit number)
64541096308152681369…50849680006044555199
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
6.454 Γ— 10¹⁰⁰(101-digit number)
64541096308152681369…50849680006044555201
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
1.290 Γ— 10¹⁰¹(102-digit number)
12908219261630536273…01699360012089110399
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.290 Γ— 10¹⁰¹(102-digit number)
12908219261630536273…01699360012089110401
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^3 Γ— origin + 1 βˆ’ 2^3 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)

What this block proved

The miner who found this block proved the existence of 8 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 8

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:57,599,680 XPMΒ·at block #6,794,454 Β· updates every 60s
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