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Block #607,778

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 6/30/2014, 6:14:01 AM Β· Difficulty 10.9071 Β· 6,201,663 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
61d4025560d12d93956ae14fafaf2bbbee71ffeea60143b9189adb77a33dd1e9
View on Chainz β†—

Height

#607,778

Difficulty

10.907096

Transactions

2

Size

432 B

Version

2

Bits

0ae83779

Nonce

164,939,054

Timestamp

6/30/2014, 6:14:01 AM

Confirmations

6,201,663

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

7f51415b683593244d9c5b5d00cb698ba46a91d72734e178fea981b05090e9d7
Transactions (2)
Coinbasea2c3267c9c4650…9ed68304120d00
1 in β†’ 1 out8.4000 XPM116 B
ANSXnLY2…Sd25TjkD
87d4e599af3ca7…048403ad42856a
1 in β†’ 2 out1.0347 XPM225 B
AbKP9Xbx…WFxDkeQeAXwQbwGg…AH1LpVEY
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.

2.210 Γ— 10⁹⁷(98-digit number)
22100378222700916811…06334202532679005179
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
2.210 Γ— 10⁹⁷(98-digit number)
22100378222700916811…06334202532679005179
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.210 Γ— 10⁹⁷(98-digit number)
22100378222700916811…06334202532679005181
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
4.420 Γ— 10⁹⁷(98-digit number)
44200756445401833622…12668405065358010359
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
4.420 Γ— 10⁹⁷(98-digit number)
44200756445401833622…12668405065358010361
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
8.840 Γ— 10⁹⁷(98-digit number)
88401512890803667244…25336810130716020719
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
8.840 Γ— 10⁹⁷(98-digit number)
88401512890803667244…25336810130716020721
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
1.768 Γ— 10⁹⁸(99-digit number)
17680302578160733448…50673620261432041439
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.768 Γ— 10⁹⁸(99-digit number)
17680302578160733448…50673620261432041441
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
3.536 Γ— 10⁹⁸(99-digit number)
35360605156321466897…01347240522864082879
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
3.536 Γ— 10⁹⁸(99-digit number)
35360605156321466897…01347240522864082881
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:57,719,598 XPMΒ·at block #6,809,440 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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