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Block #842,521

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 12/6/2014, 5:02:57 PM Β· Difficulty 10.9736 Β· 6,002,505 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
91a59b0ad9fe5b32fb2df5506fae666fcffed3be629e6713bb6b01c95dfc5fbb
View on Chainz β†—

Height

#842,521

Difficulty

10.973575

Transactions

1

Size

207 B

Version

2

Bits

0af93c39

Nonce

1,064,000,895

Timestamp

12/6/2014, 5:02:57 PM

Confirmations

6,002,505

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

8d667b04bcd9f3bf0965dde206ab15126dcb248bff99f4a9bd5a09f5d9eebba9
Transactions (1)
Coinbase8d667b04bcd9f3…5a09f5d9eebba9
1 in β†’ 1 out8.2900 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.

1.199 Γ— 10⁹⁷(98-digit number)
11993350056473939370…41782900158204518399
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
1.199 Γ— 10⁹⁷(98-digit number)
11993350056473939370…41782900158204518399
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.199 Γ— 10⁹⁷(98-digit number)
11993350056473939370…41782900158204518401
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
2.398 Γ— 10⁹⁷(98-digit number)
23986700112947878741…83565800316409036799
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.398 Γ— 10⁹⁷(98-digit number)
23986700112947878741…83565800316409036801
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
4.797 Γ— 10⁹⁷(98-digit number)
47973400225895757482…67131600632818073599
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
4.797 Γ— 10⁹⁷(98-digit number)
47973400225895757482…67131600632818073601
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
9.594 Γ— 10⁹⁷(98-digit number)
95946800451791514965…34263201265636147199
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
9.594 Γ— 10⁹⁷(98-digit number)
95946800451791514965…34263201265636147201
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
1.918 Γ— 10⁹⁸(99-digit number)
19189360090358302993…68526402531272294399
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.918 Γ— 10⁹⁸(99-digit number)
19189360090358302993…68526402531272294401
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:58,004,633 XPMΒ·at block #6,845,025 Β· updates every 60s
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