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Block #543,170

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 5/14/2014, 6:52:23 AM Β· Difficulty 10.9465 Β· 6,273,655 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
9e4f8201936a91068db5d0ee6bb9e618a1fc4a77ffc69c7c0747842c12c0d255
View on Chainz β†—

Height

#543,170

Difficulty

10.946546

Transactions

2

Size

9.49 KB

Version

2

Bits

0af250cf

Nonce

142,331,241

Timestamp

5/14/2014, 6:52:23 AM

Confirmations

6,273,655

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

f8ca428b5bcec0d91c6f64b06e70a28764562228d53d5b3edbdc7246c0a3c296
Transactions (2)
Coinbase571879c9a89622…70c163a49b6e43
1 in β†’ 1 out8.4327 XPM116 B
ANSXnLY2…Sd25TjkD
a3b278520cafa2…817c9e81173162
64 in β†’ 1 out1567.8000 XPM9.29 KB
ALMnGyhg…kpi96Xim
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.

8.763 Γ— 10⁹⁷(98-digit number)
87633907695748057123…38287288167434393319
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
8.763 Γ— 10⁹⁷(98-digit number)
87633907695748057123…38287288167434393319
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
8.763 Γ— 10⁹⁷(98-digit number)
87633907695748057123…38287288167434393321
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
1.752 Γ— 10⁹⁸(99-digit number)
17526781539149611424…76574576334868786639
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.752 Γ— 10⁹⁸(99-digit number)
17526781539149611424…76574576334868786641
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
3.505 Γ— 10⁹⁸(99-digit number)
35053563078299222849…53149152669737573279
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
3.505 Γ— 10⁹⁸(99-digit number)
35053563078299222849…53149152669737573281
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
7.010 Γ— 10⁹⁸(99-digit number)
70107126156598445698…06298305339475146559
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
7.010 Γ— 10⁹⁸(99-digit number)
70107126156598445698…06298305339475146561
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
1.402 Γ— 10⁹⁹(100-digit number)
14021425231319689139…12596610678950293119
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.402 Γ— 10⁹⁹(100-digit number)
14021425231319689139…12596610678950293121
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:57,778,640 XPMΒ·at block #6,816,824 Β· updates every 60s
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